Equalize using linear equalizer that updates weights with variable-step-size LMS algorithm
The Variable Step LMS Linear Equalizer block uses a linear equalizer and the variable-step-size LMS algorithm to equalize a linearly modulated baseband signal through a dispersive channel. During the simulation, the block uses the variable-step-size LMS algorithm to update the weights, once per symbol. When you set the Number of samples per symbol parameter to 1, then the block implements a symbol-spaced equalizer and updates the filter weights once for each symbol. When you set the Number of samples per symbol parameter to a value greater than 1, the weights are updated once every Nth sample, for a T/N-spaced equalizer.
The Input port accepts a column vector input signal. The Desired port receives a training sequence with a length that is less than or equal to the number of symbols in the Input signal. Valid training symbols are those symbols listed in the Signal constellation vector.
Set the Reference tap parameter so it is greater than zero and less than the value for the Number of taps parameter.
The Equalized port outputs the result of the equalization process.
You can configure the block to have one or more of these extra ports:
Mode input, as described in Reference Signal and Operation Modes in Communications System Toolbox™ User's Guide.
Err output for the error signal, which is the difference between the Equalized output and the reference signal. The reference signal consists of training symbols in training mode, and detected symbols otherwise.
Weights output, as described in Adaptive Algorithms in Communications System Toolbox User's Guide.
To learn the conditions under which the equalizer operates in training or decision-directed mode, see Adaptive Algorithms in Communications System Toolbox User's Guide.
For proper equalization, you should set the Reference tap parameter so that it exceeds the delay, in symbols, between the transmitter's modulator output and the equalizer input. When this condition is satisfied, the total delay, in symbols, between the modulator output and the equalizer output is equal to
1+(Reference tap-1)/(Number of samples per symbol)
Since the channel delay is typically unknown, a common practice is to set the reference tap to the center tap.
The number of taps in the filter of the linear equalizer.
The number of input samples for each symbol.
A vector of complex numbers that specifies the constellation for the modulation.
A positive integer less than or equal to the number of taps in the equalizer.
The step size that the variable-step-size LMS algorithm uses at the beginning of the simulation.
The increment by which the step size changes from iteration to iteration
The smallest value that the step size can assume.
The largest value that the step size can assume.
The leakage factor of the LMS algorithm, a number between 0 and 1. A value of 1 corresponds to a conventional weight update algorithm, and a value of 0 corresponds to a memoryless update algorithm.
A vector that lists the initial weights for the taps.
When you select this check box, the block has an input port that allows you to toggle between training and decision-directed mode. For training, the mode input must be 1, for decision directed, the mode should be 0. For every frame in which the mode input is 1 or not present, the equalizer trains at the beginning of the frame for the length of the desired signal.
When you select this check box, the block outputs the error signal, which is the difference between the equalized signal and the reference signal.
When you select this check box, the block outputs the current weights.
 Farhang-Boroujeny, B., Adaptive Filters: Theory and Applications, Chichester, England, Wiley, 1998.